From codim 2 to equilibria

• From codim 2 to equilibria
• • From Bogdanov-Takens (BT) point to Fold / Hopf curve
  • From Zero-Hopf (ZH) point to Fold / Hopf curve
  • From Hopf-Hopf (HH) point to Fold / Hopf curve

From Bogdanov-Takens (BT) point to Fold / Hopf curve

We provide an automatic branch switching method in this case (see for example Extended Lorenz-84 model or 2d Ginzburg-Landau equation (finite differences, codim 2, Hopf aBS)). Hence, you can perform automatic branch switching by calling continuation with the following options:

continuation(br::ContResult, ind_BT::Int,
	options_cont::ContinuationPar = br.contparams;
	nev = options_cont.nev,
	detect_codim2_bifurcation::Int = 0,
	start_with_eigen = false,
	autodiff = false,
	Teigvec = getvectortype(br),
	scaleζ = norm,
	kwargs...)

where ind_BT is the index of the BT point in br. Note that the BT has been detected during Fold or Hopf continuation. Calling the above method thus switches from Fold continuation to Hopf continuation (and vice-versa) automatically with the same parameter axis.

Check the docs of Fold / Hopf Continuation and particularly Setting the jacobian for improving the speed of computation for large scale systems.

From Zero-Hopf (ZH) point to Fold / Hopf curve

We provide an automatic branch switching method in this case (see for example Extended Lorenz-84 model or 2d Ginzburg-Landau). Hence, you can perform automatic branch switching by calling continuation with the following options:

continuation(br::ContResult, ind_ZH::Int,
	options_cont::ContinuationPar = br.contparams;
	nev = options_cont.nev,
	detect_codim2_bifurcation::Int = 0,
	start_with_eigen = false,
	autodiff = false,
	Teigvec = getvectortype(br),
	scaleζ = norm,
	kwargs...)

where ind_ZH is the index of the ZH point in br. Note that the ZH has been detected during Fold or Hopf continuation. Calling the above method thus switches from Fold continuation to Hopf continuation (and vice-versa) automatically with the same parameter axis.

Check the docs of Fold / Hopf Continuation and particularly Setting the jacobian for improving the speed of computation for large scale systems.

From Hopf-Hopf (HH) point to Fold / Hopf curve

We provide an automatic branch switching method in this case (see for example Extended Lorenz-84 model or 2d Ginzburg-Landau equation). Hence, you can perform automatic branch switching by calling continuation with the following options:

continuation(br::ContResult, ind_HH::Int,
	options_cont::ContinuationPar = br.contparams;
	δp = nothing, ampfactor::Real = 1,
	nev = options_cont.nev,
	detect_codim2_bifurcation::Int = 0,
	start_with_eigen = false,
	autodiff = false,
	Teigvec = getvectortype(br),
	scaleζ = norm,
	kwargs...)

where ind_HH is the index of the HH point in br. Note that the HH has been detected during Hopf continuation. Calling the above method thus switches from Hopf continuation to another Hopf branch automatically with the same parameter axis.

Check the docs of Fold / Hopf Continuation and particularly Setting the jacobian for improving the speed of computation for large scale systems.